How-to guides · 3 min read
Order of Operations: Why PEMDAS Trips People Up
What PEMDAS and BODMAS really say
PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) and BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction) are the same rules. The letters are a memory aid; the important part is that multiplication and division share one level, as do addition and subtraction.
Within a level you work left to right. Learners who treat “M” as always before “D” get 8 ÷ 2 × 4 wrong: it is 16, not 1.
Watch the order: brackets first, then left to right
Order-of-operations steps 3 steps
Start: 8 ÷ 2 × (2 + 2)
- Add
2 + 2 = 4→ 8 ÷ 2 × 4 - Divide
8 ÷ 2 = 4→ 4 × 4 - Multiply
4 × 4 = 16→ 16
Where the viral puzzles go wrong
Expressions like 6 ÷ 2(1 + 2) spark arguments because of implicit multiplication — the “2(…)” with no × sign. Some textbooks bind it tighter than ordinary division; others do not. CalcSolver Pro treats it as normal multiplication in left-to-right order and returns 9.
Unary minus and exponents
Exponents bind tighter than a leading minus sign, so −2² means −(2²), which is −4. If you want the square of negative two, write (−2)².
Exponent first, then the minus
Order-of-operations steps 2 steps
Start: −2^2
- Exponent
2^2 = 4→ −4 - Negate
−4 = −4→ −4
A habit that prevents most mistakes
- Add brackets whenever a reader could misread the order.
- Work left to right inside each level.
- Check with a calculator that shows steps, so you can see which operation happened first.
Frequently asked questions
Is PEMDAS the same as BODMAS?
Yes. They describe the same order; only the names and the order of the letters differ between countries.
Does multiplication always come before division?
No. They share a level and are done left to right, as are addition and subtraction.
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